PSEB 8th Class Maths Solutions Chapter 9 Algebraic Expressions and Identities Ex 9.2

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 9 Algebraic Expressions and Identities Ex 9.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.2

1. Find the product of the following pairs of monomials:

Question (i)
4, 7p
Solution:
= 4 × 7p
= 4 × 7 × p
= 28p

Question (ii)
– 4p, 7p
Solution:
= – 4p × 7p
= (-4 × 7) × p × p
= – 28p²

Question (iii)
– 4p, 7pq
Solution:
= (- 4p) × 7pq
= – 4 × 7 × p × pq
= – 28p²q

Question (iv)
4p³, – 3p
Solution:
= 4p³ × (- 3p)
= 4 × (- 3) × p³ × p
= – 12p⁴

Question (v)
4p, 0
Solution:
= 4p × 0
= 0

2. Find the areas of rectangles with the following pairs of monomials as their s lengths and breadths respectively:
(p, q); (10m, 5n); (20x², 5y²); (4x, 3x²); (3mn, 4np)
Solution:
Area of a rectangle = length × breadth
(i) length = p, breadth = q
∴ Area = length × breadth
= p × q = pq unit²

(ii) length = 10m, breadth = 5n
∴ Area = length × breadth
= 10m × 5n
= 50mn unit²

(iii) length = 20x², breadth = 5y²
∴ Area = length × breadth
= 20x² × 5y²
= 100x²y² unit²

(iv) length = 4x, breadth 3x²
∴ Area = length × breadth
= 4x × 3x²
= 12x³ unit²

(v) length = 3mn, breadth = 4np
∴ Area = length × breadth
= 3mn × 4np
= 12 mn²p unit²

3. Complete the table of products:
Solution:

First monomial → Second monomial ↓	2x	-5 y	3x2	-4xy	7x2y	– 9x2y2
2x	4x2	-10xy	6x3	-8x2y	14x3y	– 18x3y2
– 5 y	– 10xy	25y2	– 15x2y	20xy2	– 35x2y2	45x2y3
3x2	6x3	– 15x2y	9x4	– 12x3y	21x4y	– 27x4y2
– 4xy	– 8x2y	20xy2	-12x3y	16x2y2	– 28x3y2	36x3y3
7x2y	14x3y	– 35x2y2	21x4y	– 28x3y2	49x4y2	– 63x4y3
– 9x2y2	– 18x3y2	45x2y3	– 27x4y2	36x3y3	– 63x4y3	81x4y4

4. Obtain the volume of rectangular boxes with the following length, breadth and height respectively:

Question (i)
5a, 3a², 7a⁴
Solution:
Volume of rectangular box = length × breadth × height
length = 5a, breadth = 3a², height = 7a⁴
∴ Volume = length × breadth × height
= 5a × 3a² × 7a⁴
= (5 × 3 × 7) × a × a² × a⁴
= 105a⁷ cubic unit

Question (ii)
2p, 4q, 8r
Solution:
length = 2p, breadth = 4q, height = 8r
∴ Volume = length × breadth × height
= 2p × 4q × 8r
= (2 × 4 × 8) × p × q × r
= 64pqr cubic unit

Question (iii)
xy, 2x²y, 2xy²
Solution:
length = xy, breadth = 2x²y, height = 2 xy²
∴ Volume = length × breadth × height
= xy × 2x²y × 2xy²
= (1 × 2 × 2) × xy × x²y × xy²
= 4x⁴y⁴ cubic unit

Question (iv)
a, 2b, 3c
Solution:
length = a, breadth = 2b, height = 3c
∴ Volume = length × breadth × height
= a × 2b × 3c
= (1 × 2 × 3) × a × b × c
= 6abc cubic unit

5. Obtain the product of:

Question (i)
xy, yz, zx
Solution:
= xy × yz × zx
= [x × y) × (y × z) × (z × x)
= x × x × y × y × z × z
= x²y²z²

Question (ii)
a, -a², a³
Solution:
= (a) × (- a²) × (a³)
= – a × a² × a³
= – a⁶

Question (iii)
2, 4y, 8y², 16y³
Solution:
= 2 × 4y × 8y² × 16y³
= 2 × 4 × 8 × 16 × y × y² × y³
= 1024y⁶

Question (iv)
a, 2b, 3c, 6abc
Solution:
= a × 2b × 3c × 6abc
= 1 × 2 × 3 × 6 × a × b × c × abc
= 36 a²b²c²

Question (v)
m, – mn, mnp
Solution:
= (m) × (- mn) × (mnp)
= – (m × mn × mnp)
= – m³n²p